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Differentiating Powers of x (1 of 4: Reviewing the Fundamentals)
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Introduction to Differentiation
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- 1 Prologue to Calculus (1 of 5: How fast did Usain Bolt run?)
- 2 Prologue to Calculus (2 of 5: How can we measure more accurately?)
- 3 Prologue to Calculus (3 of 5: The difference quotient)
- 4 Prologue to Calculus (4 of 5: Exploring a parabola)
- 5 Prologue to Calculus (5 of 5: Gradient of the tangent)
- 6 Basics of Calculus (1 of 5: Foundational language & notation)
- 7 Basics of Calculus (2 of 5: Example of using first principles)
- 8 Basics of Calculus (3 of 5: Observing patterns in first principles)
- 9 Basics of Calculus (4 of 5: Considering the gradient function visually)
- 10 Basics of Calculus (5 of 5: Locating a tangent)
- 11 Calculus Notation & Terminology
- 12 First Principles Example: Square Root of x
- 13 First Principles Example: x²
- 14 First Principles Example: x³
- 15 First Principles for the Gradient Function
- 16 Prologue to Calculus
- 17 Calculus - Important Results (1 of 2)
- 18 Calculus - Important Results (2 of 2)
- 19 Chain Rule
- 20 Proving Product Rule
- 21 Quotient Rule
- 22 Why We Need The Product Rule
- 23 Product Rule - example question
- 24 Review - Basic Differentiation Rules
- 25 Continuity
- 26 Overview of Differentiation Rules
- 27 Differentiating the fourth root of x (by first principles)
- 28 Linear Rate of Change: Inlet+Outlet Valve Question
- 29 Linear Rate of Change: 2 Inlet Valves Question
- 30 What are Limits? (1 of 3: Approaching from Different Sides)
- 31 What are Limits? (2 of 3: A More Rigorous Definition)
- 32 What are Limits? (3 of 3: One Strategy for Evaluating Limits)
- 33 What is Continuity? (1 of 2: Definitions)
- 34 What is Continuity? (2 of 2: An Interesting Counter-Example)
- 35 Introduction to Calculus (1 of 2: Seeing the big picture)
- 36 Introduction to Calculus (2 of 2: First Principles)
- 37 Applying First Principles to x² (1 of 2: Finding the Derivative)
- 38 Applying First Principles to x² (2 of 2: What do we discover?)
- 39 Applying First Principles to x³
- 40 Finding the Equation of a Tangent
- 41 Deriving a Rule for Differentiating Powers of x
- 42 Differentiating Powers of x (1 of 4: Reviewing the Fundamentals)
- 43 Differentiating Powers of x (2 of 4: Considering the Hyperbola)
- 44 Differentiating Powers of x (3 of 4: First Principles & the Hyperbola)
- 45 Derivatives of Odd & Even Functions
- 46 Differentiating Powers of x (4 of 4: Square Root of x)
- 47 The Derivative of a Sum
- 48 Function of a Function Rule (1 of 4: Expanding Before Differentiating)
- 49 Function of a Function Rule (2 of 4: Introducing a Substitution)
- 50 Function of a Function Rule (3 of 4: Simple Example)
- 51 Function of a Function Rule (4 of 4: Working with Square Roots)
- 52 Product Rule (1 of 2: It's Complicated...)
- 53 Product Rule (2 of 2: Simple Example)
- 54 Where does the Product Rule come from? (1 of 2: Delta Notation)
- 55 Where does the Product Rule come from? (2 of 2: Derivation)
- 56 Quotient Rule (1 of 2: Derivation)
- 57 Quotient Rule (2 of 2: Simple Example)
- 58 Differentiability (1 of 3: Cube root of x)
- 59 Differentiability (2 of 3: Absolute Value of x)
- 60 Differentiability (3 of 3: x to the power of 2/3)
- 61 Differentiability (Formal Definition)
- 62 Properties of a Piecemeal Function (1 of 2: Testing Continuity)
- 63 Properties of a Piecemeal Function (1 of 2: Testing Differentiability)
- 64 Fundamental Definitions of Speed & Velocity
- 65 Instantaneous Velocity/Acceleration (1 of 2: Defining the Concepts)
- 66 Instantaneous Velocity/Acceleration (2 of 2: Example question)
- 67 Limits & Continuity (1 of 3: Formal intro to limits)
- 68 Limits & Continuity (2 of 3: Limits that exists when functions don't)
- 69 Limits & Continuity (3 of 3: Applications to graphs)
- 70 Continuity: Definitions & basic concept
- 71 The Problem of Tangents (1 of 4: Gradient as a function)
- 72 The Problem of Tangents (2 of 4: First Principles)
- 73 The Problem of Tangents (3 of 4: Gradient function of x²)
- 74 Applications of First Principles (1 of 4: Refining language and notation)
- 75 The Problem of Tangents (4 of 4: Finding a tangent's equation)
- 76 Applications of First Principles (2 of 4: The function 1/x)
- 77 Applications of First Principles (3 of 4: The function √x)
- 78 Applications of First Principles (4 of 4: Developing the power rule)
- 79 Product Rule (1 of 2: Derivation)
- 80 Review of Differentiation Rules
- 81 Product Rule (2 of 2: Applying it to example functions)
- 82 Quotient Rule (1 of 2: Derivation)
- 83 Quotient Rule (2 of 2: Examples & warnings)
- 84 Differentiating a Rational Function by First Principles
- 85 Finding the equation of a normal at a given point
- 86 Differentiating with Product & Chain Rule (example question)
- 87 The Differential Operator (1 of 2: Introduction to notation)
- 88 The Differential Operator (2 of 2: Example question)
- 89 Angle of Inclination (with Calculus)
- 90 Power Rule for Differentiation (1 of 4: Conjecture)
- 91 Power Rule for Differentiation (2 of 4: Background knowledge)
- 92 Power Rule for Differentiation (3 of 4: Derivation of rule)
- 93 Power Rule for Differentiation (4 of 4: Hyperbola)
- 94 Basics of Calculus, continued (1 of 2: Sum of functions)
- 95 Basics of Calculus, continued (2 of 2: Multiples of functions, constant function)
- 96 Leibniz's Derivative Notation (1 of 3: Overview)
- 97 Leibniz's Derivative Notation (2 of 3: Finding equation of a tangent)
- 98 Leibniz's Derivative Notation (3 of 3: Introducing the chain rule)
- 99 Using the Chain (Function of a Function) Rule
- 100 Product Rule - Definition
- 101 Quotient Rule (1 of 2: Proof from product & chain rule)
- 102 Quotient Rule (2 of 2: Worked examples)
- 103 Motion Graphs (1 of 2: Cannon Man's Displacement)
- 104 Motion Graphs (2 of 2: Cannon Man's Speed)
- 105 Review of Basic Differentiation (1 of 2: Polynomials, Products, Quotients)
- 106 Review of Basic Differentiation (2 of 2: Considering derivatives visually)
- 107 Calculus of Exponential Functions (1 of 4: Considering derivatives visually)
- 108 Calculus of Exponential Functions (2 of 4: The importance of 2.718...)
- 109 Calculus of Exponential Functions (3 of 4: Basic differentiation examples)
- 110 Calculus of Exponential Functions (4 of 4: Differentiating with non-e bases)
- 111 Determining Derivatives from Graphs (1 of 3: Identifying major features)
- 112 Determining Derivatives from Graphs (2 of 3: Considering sign of the gradient)
- 113 Determining Derivatives from Graphs (3 of 3: Reversing the process)